ON THE DETERMINATION OF DENSITY PROFILES IN STRATIFIED SEAS FROM KINEMATICAL PATTERNS OF SHIP-INDUCED INTERNAL WAVES

The aim of this paper is to propose a method for determining the dispe rsion relation of a highly stratified medium from measured geometrical patterns of ship-generated internal waves. This is a first step towar ds devising a practical method for calculating the density distributio n of a stratified fluid from the detectable free-surface kinematic sig nature of the induced internal wake, by using some optical or remote s ensing means. We assume that the body which causes the wake moves with a constant velocity along a circular trajectory. By applying the cons tant-phase method, we derive an explicit solution for the wake crest l ines. Then, for an infinitely large ship's turning radius (straight co urse), a closed-form expression for the dispersion relation versus wak e geometry is obtained. A similar approximate form is also obtained fo r a circular course. Some numerical simulations are presented, and the applicability of the proposed method is demonstrated for several real istic thermocline distributions, measured in lakes and seas.